For an acute angle θ with 3sinθ = 4cosθ, the value of (4sinθ − 3cosθ)/(2sinθ + 6cosθ) is:

The condition says tanθ = 4/3, so sinθ = 4/5 and cosθ = 3/5. The numerator is 16/5 − 9/5 = 7/5 and the denominator is 8/5 + 18/5 = 26/5, giving 7/26. Reading the ratio upside down as tanθ = 3/4 makes the numerator vanish and suggests 0; cancelling the ratios and using the bare coefficients gives 1/8; and inverting the finished fraction gives 26/7.